Aerospace Engineering and Mechanics

**It is well known that crystal plasticity is the result of the presence
and motion of dislocations in a body, manifesting itself through stress,
permanent and recoverable deformation, and work hardening of the material.
Stress and recoverable deformation arise due to the elastic lattice stretching
induced by applied loads and the presence of dislocations; permanent
deformation is the result of the motion of dislocations through the lattice;
and hardening arises from short and long range elastic interactions, i.e.
combine stress effects of a distribution of dislocations in the body, that tend
to decrease the ductility (increased strength) of the material.**

**Despite the many successes of conventional and gradient theories of
single crystal plasticity, a field theory that allows for the calculation of
stress fields of evolutionary 3-d dislocation distributions in finite bodies
under nominally unrestricted deformations and loads, large lattice rotations
and nonlinear crystal elasticity is still a research goal.**

**This presentation elaborates on the development of such a theory and
presents some of the simplest consequences of it that seem to suggest that the
theory has the potential of describing dislocation plasticity at small scales.
In particular, stress fields of a screw dislocation in a linear elastic and
neo-Hookean material, the development of a slip step due to exit of an edge
dislocation from a crystal, kinematics of rectilinear motion of a straight
dislocation and expansion of a polygonal loop, and the kinematics of the
initiation of bowing and cross-slip of dislocation segments will be discussed.
Driving forces for dislocation motion representing the nature of Schmid and
non-Schmid effects arising from dislocation behavior as well as a non-local
driving force for dislocation nucleation, as these arise as (non-local)
thermodynamic consequences of the theory, will also be discussed.**

**But what of observed plasticity at coarser scales of resolution? Is it
possible to invoke some homogenization procedure for nonlinear evolutionary
field equations that may be used to derive a coarse scale theory corresponding
to the fine scale dislocation mechanics described above? Time permitting, a
candidate procedure based on an application of Muncaster's 'Formal theory of
invariant manifolds in mechanics' will be illustrated through two simple
examples from phenomenological plasticity and dislocation mechanics.**

209 Akerman Hall

2:30-3:30 p.m.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior Secretary, 625-8000.